A stabilized finite element method based on two local Gauss integrations for the Stokes equations

This paper considers a stabilized method based on the difference between a consistent and an under-integrated mass matrix of the pressure for the Stokes equations approximated by the lowest equal-order finite element pairs (i.e., the P1-P1 and Q1-Q1 pairs). This method only offsets the discrete pressure space by the residual of the simple and symmetry term at element level in order to circumvent the inf-sup condition. Optimal error estimates are obtained by applying the standard Galerkin technique. Finally, the numerical illustrations agree completely with the theoretical expectations.